P2 is co-pilot on a multicrew aircraft unless you have been working for an AOC holder with CAA approval its impossible to log this on a single pilot aircraft.

P1U/S is PICUS which can only be logged during a skills test which is successful with an examiner. This does not include club check outs or anything else you have done with a plain instructor sitting next to you. It can only be logged for rating and license flight exams.

P1U/S or PICUS can also be logged in multicrew environment by co-pilots if several conditions are met (don't go there on this one because it can get contentious and it only really matters once you flying multicrew)